From Dubrovnik to Albanian Border distance is approximately 180 kilometers and it takes at least 3,5 hours. There is no direct bus lines between Dubrovnik and Albania, so you can use local bus service or private transfers to reach Montenegro and then from Montenegro try to catch some buses to Tirana.

I had some customers from Dubrovnik to Albanian border last summer, and they arranged a private transfers service from Albanian border to Tirana (or Durres not sure), but I was told it is not expensive.

Contact your host in Albania and ask for transfers possibilities from Montenegro.